Apparatus and method for determining the range and bearing in a plane of an object characterized by an electric or magnetic dipole

ABSTRACT

Orthogonal components of electromagnetic field perturbations due to objects characterized by electric or magnetic dipoles are measured along orthogonal axes in a plane. The components are proportional with (3 cos 2  θ-1) and (3 cos θ sin θ), where θ is the bearing of the dipole center relative to the device for measuring the field components. θ is readily determined from these equations and the range of the object can also be determined from knowledge of the dipole moment.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to means and methods for determining magnetic andelectric fields using gradiometers, magnetometers, or electrometers.More particularly, perturbations in magnetic and electric fields due tomagnetic or electric dipoles are sensed with electric or magneticgradiometers.

2. Prior Art

Many devices for measuring magnetic field direction, locating objects ordetermining the orientation of an object by measuring electromagneticfields have been proposed. Among these are U.S. Pat. Nos. 3,061,239 toS. J. Rusk, 3,644,825 to P.D. Davis, Jr. et al, 3,728,525 to C. K.Adkar, 4,267,640 to C. T. Wu, 4,287,809 to W. H. Egli, et al, 4,302,746to J. F. Scarzello, et al and 4,314,251 to F. H. Raab.

Raab uses generalized matrix formulations as the basis for a system ofradiating and receiving antennas which determine the position andorientation of a remote object. The transmitter employs two orthogonalradiating antennas and the receiver has three mutually orthogonalreceiving antennas. The transmitting antennas should be magnetic dipolesources. Raab discloses only the intentional excitation of transmissionloops by periodic signals. His equations for determining position andorientation are of the most general form (e.g. equation 27 is a generalproduct matrix for three orthogonal rotations) and are quite complex.

Similarly the Egli, et al patent determines orientation and position ofa helmet with a system having transmitting and receiving antennas byemploying generalized matrix formulations.

Rusk discloses a static magnetic moment device for maintaining asatellite in a predetermined orientation with respect to its orbit aboutthe earth. Rusk makes use of the torque produced by the magneticinteraction between the earth's magnetic field and a predeterminedmagnetic field developed on the satellite in response to attitudecontrol signals derived from conventional vehicle attitude detectiondevices. Three mutually perpendicular magnetic torquing coils areutilized.

Wu measures a magnetic field with crossed rods each having a rectangularshaped B-H hysteresis curve. The earth's field biases each rod so thatthe B field of each will switch between a high and low state withvoltages in direct proportion to the component of the earth's field linealong each rod.

Scarzello, et al uses a two axis magnetometer to sense a vehicle'smagnetic signature. Standard two axis magnetometers or gradiometers withwindings on ring cores are integrated in a system to sense the arrivaland exit of a vehicle at a fixed location. Comparisons to predeterminedthresholds are made to screen against electromagnetic interferenceeffects and false alarms.

Adkar determines the geographical location of an object on the earth byimposing known perturbations of magnetic flux first on the verticalcomponent of the earth's field and then on an orthogonal component lyingin a horizontal plane at the earth's surface. Knowledge of total fieldstrength allows the determination of location, inclination and azimuth.

Davis, Jr., et al uses two magnetic field sensors to generate outputsignals representative of perpendicular directional components of avarying magnetic field. Each output signal is differentiated andcircuitry multiplies each output signal by the differential of the otheroutput signal. The multiplication products are substracted to produce aresultant signal. The polarity and magnitude of the resultant signal issensed to determine either direction of movement of the object creatingthe magnetic field, or to indicate the relative position of the objectwith respect to the sensors if the direction of movement of the objectis known.

Also known are the field equations for magnetic induction B(r) due to amagnetic dipole, i.e.: ##EQU1## where r is the direction vector betweenan origin on the dipole and the point of observation, u is a unit vectorfrom the origin in the direction of r and m is the magnetic momentdefined by: ##EQU2## for a current distribution J (see FIG. 1). For aferromagnetic material m is the sum of a permanent magnetic moment andan induced magnetic moment.

Similar equations hold for the electric field E(r) due to a dipole ofelectric dipole moment p, i.e. ##EQU3## where ρ is a chargedistribution.

None of the above systems provide for the determination in a plane (fromtwo orthogonal magnetic field components due to the perturbation of anexternal magnetic field by the magnetic dipole) of the angularorientation of a magnetic dipole relative to a point of observation witha single equation having one independent variable. Nor do such prior artsystems provide for the same determination from perturbations of anelectric field due to an electric dipole.

SUMMARY OF THE INVENTION

This invention discloses a method of determining, with a device formeasuring magnetic field perturbation, the bearing θ of a ferromagneticmaterial located in a region subject to an external magnetic field ofknown strength and direction within the region, where θ is the anglebetween a line from the measuring device to the location of theferromagnetic material and a first direction, the first direction beingthe direction of the external magnetic field at the location of theferromagnetic material, comprising: determining a first component of theperturbation of the external magnetic field at the site of the measuringdevice along the first direction, determining a second component of theperturbation of the external magnetic field at the site of the measuringdevice along a direction orthogonal to the first direction and lying inthe plane, forming a first equation by setting the first component equalto (3 cos² θ-1), forming a second equation by setting the secondcomponent equal to (3 cos θ sin θ), forming a ratio of the first andsecond equations thereby yielding a third equation, and determining θfrom the third equation.

Similar methods, where perturbations of an external electric field dueto an electric dipole provide the first and second components, are alsodisclosed.

Means corresponding to the above methods comprise further aspects of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the geometry for calculating a current distribution.

FIG. 2A indicates the coordinate system used to describe the presentinvention.

FIG. 2B indicates unit vectors lying along the coordinate axes of FIG.2A.

FIG. 3 is a schematic representation of a portion of a dipole field dueto an electric or magnetic dipole.

FIG. 4 illustrates a refinement in the coordinate system used todescribe the present invention.

FIG. 5 illustrates a device according to the present invention.

FIG. 6 illustrates two alternative methods of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The Cartesian coordinates x,y,z of FIG. 2A with Origin O (and unitvectors i,j,k of FIG. 2B) are selected with the x,y, plane forming theplane in which measurements are made. O is located within the boundriesof a ferromagnetic material, current distribution or charge distribution(identified in FIG. 2A as object 10). For distances far enough away fromobject 10, (i.e., generally at least several radii of object 10), themagnetic or electric field due to object 10 can be characterized as anelectric dipole field (for a charge distribution) or a magnetic dipolefield (for current distributions and material which will form inducedmagnetic dipoles or possess permanent magnetic dipoles). For simplicity,the dipole moment of the electric or magnetic field is chosen tocoincide with the x axes. In FIG. 2a, for illustrative purposes, amagnetic dipole moment m_(H) is depicted. The direction of m_(H) will ingeneral form an angle θ in the x-y plane with a line from O to a point Pat which field readings will be taken. The cord OP is defined as R.

For ferromagnetic materials and current distributions, m_(H) representsthe induced magnetic dipole due to an external magnetic field H_(o).Cartesian coordinates are chosen in FIG. 1 so that H_(o) lies in the x-zplane, which is physically consistent with selecting m_(H) to lie alongthe x axis. The magnetic field in the x-y plane (H_(xy)) thus reduces tothe x component of H_(o) (i.e., H_(x)). When object 10 is aferromagnetic material, m_(H) may not be the only magnetic dipolecomponent. Particularly in objects including "hard iron", in addition tom_(H) there will be a permanent magnetic dipole moment having acomponent m_(o) in the x-y plane. In general the direction of m_(o) andm_(H) will form an angle α in the x-y plane. The analysis below assumesm_(H) is much larger than m_(o). H will be used for H_(x) forsimplicity. The magnetic dipole case will be discussed first with theelectric dipole case addressed later.

A ferromagnetic material (i.e., object 10) is modeled thus: under anexternal magnetic field H, object 10 "resonates" and becomes a magneticdipole of value:

    m=H.sub.o d.sup.3                                          (5)

where d represents the characteristic magnetic diameter of object 10 andis given by: ##EQU4## where V=volume of object 10,

μ=magnetic permeability and

N/4π=demagnetizing factor.

Assume object 10 to be confined to the x-y lane and H is the x-ycomponent of H_(o). Then, from equation 1, the field perturbation fsensed by a magnetometer 12 (see FIG. 3) at point P a distance R=|R|from object 10 is: ##EQU5## where: u=unit vector along R

uu="outer-square" of u, a symmetric matrix

and

I=identity matrix.

Since H equals iH, equation 4 becomes: ##EQU6##

Further, because

    μ=i cos θ+j sin θ                           (9)

and

    μ.i=cos θ                                         (10)

equation 5 becomes:

    f=Hd.sup.3 /R.sup.3 (i(3 cos.sup.2 θ-1)+j 3 cos θ sin θ) (11).

One can solve for θ in terms of the ratio of i and j components of f asfollows: ##EQU7## which leads to:

    τ.sup.2 +3λτ-2=0                            (13)

where τ=tan θ.

The solution for τ is thus: ##EQU8## and sin θ and cos θ are given by##EQU9##

Note that equation 12 could be formed as λ⁻¹, then Z in equation 14would be 3/(2λ).

If d is known, equation 8 will readily yield R from: ##EQU10##

Denoting magnetic field perturbations in the x and y directions due toobject 10 as B_(x) and B_(y), respectively, from equation 8: ##EQU11##

R and θ for electric field perturbations due to a charge distributioncan be computed by the same analysis employing equation 3 and 4. R and θfor current distributions are similarly determined using equation 2.

Typically, a two axis magnetometer would be used to measure B_(x) andB_(y). If a first axis of the magnetometer is aligned with H, then (forexample) B_(x) equals H. If the first axis and H form an angle β, wherethe first axis lies along a direction x' and H lies along the x axis, Hcould be resolved into components along x and y or a standard coordinatetransformation between x' and x would be employed (see FIG. 4). In orderfor two axis magnetometer 12 to measure field perturbations, thehorizontal external field components (i.e., Hx and Hy) at 0 prior to thepresence of object 10 must be known and substracted from measurements ofBx and By when object 10 is present. It is also possible to adapt amagnetic gradiometer to measure field perturbation components directly.

FIG. 3 shows a schematic of a typical plot of magnetic field lines 14representing perturbations in the external magnetic field H due to theinduced magnetic dipole m_(H) of object 10.

Measurements can be made with β being nonzero but for convenience anaxis of magnetometer 12 will be aligned with the x axis so that β iszero. This simplifies the equations.

An example of a device 16 to generate θ and R employing measuring device12 is shown in FIG. 5. Measuring device 12 (for magnetic fields it ispreferably a magnetometer) measures components Hx and Hy with object 10not present and with object 10 present. Computer 18 retains theunperturbated values of <Hx> and <Hy> in averager 19 (or its main memory20). Computer 18 employs substractor 22 to subtract the unperturbatedvalues of <Hx> and <Hy> from the values of Hx and Hy, respectively, withobject 10 present. This yield Bx and By, the perturbated fieldcomponents. Computer 18 further includes λ generator 24, τ generator 26and θ determinator 28. λis found directly from B_(x) and B_(y) and τ isfound directly from τ. A convenient way to determine θ is to employ alookup table approach. Memory 20 will then contain values for arctan πin memory 20. Once θ is known, servomechanism 30 can be adapted toperform a variety of functions.

R is provided by R generator 32 from a knowledge of θ and d. Againmemory 20 can hold values for d for an object 10 having a known magneticcharacteristic diameter or being of an expected magnetic characteristicdiameter. Servomechanism 30 can be employed to perform a variety offunctions dependent on the value of R.

In weapon systems applications, servomechanism 30 can be adapted to firea weapon (not shown) along a direction determined by θ, or provide anomnidirectional blast at a range R or fire a weapon along a directionand at a range determined by θ and R. A triggering mode can be providedby aligning a weapon along a critical angle with respect to thedirection of H. That angle would be identified as γ crit. When θ equalsγ crit, servomechanism 30 could activate a weapon. Comparator 34 can beemployed to compare θ to γ crit. Similarly a critical range (R crit)could be used to trigger an omnidirectional blast when R equals R crit.

The lookup approach depicted in FIG. 5 is only one method of computingθ. Computer 18 could, for example, compute θ directly from λ using aniterative process.

A method of determining R and θ is summarized in FIG. 6. The step ofdetermining θ directly from λ is shown (in the righthand column of FIG.6) to be alternatively accomplished by first generating τ.

In the above discussion it was assumed that the magnitude and directionof H is substantially constant over the region including object 10 andmagnetometer 12. This allowed H to be set equal to iH in equation (8).If there is some variance between the direction or magnitude of H at thelocation of object 10 and at the site of magnetometer 12, it ispreferable to use the method of the present invention to determine afirst value of R and θ with H equal to H at the site of magnetometer 12.Since it is assumed that the magnitude and direction of H is known atall points, the value of H at this first location defined by R and θ isknown and is then used to compute a second R and θ. The process can berepeated in an iterative manner for further accuracy with the value of Hfor each new computation being the value of H at the location determinedby the last computed values of R and θ.

If m_(H) is not much larger than m_(o), the true magnetic field lines(see 36 in FIG. 4) due to object 10 will not coincide with lines 14. Inthat event the net magnetic dipole will be represented by the vector sumof m_(o) and m_(H). In general, the net magnetic dipole moment will forman angle in the x-y plane with H. A dipole field will still begenerated, however the angle between the magnetic dipole moment and thecomponent of H_(o) in the xy plane will not be known. The device andmethod of the present invention can still be employed to determine thetrue locations of the center of the dipole by passively tracking overtime, the curvature (i.e., |B_(x) |/|B_(y) |) of the perturbated fieldline with measuring device 12. Given this tracking information, the datacan be fitted to curves representing different dipole models so that thetrue center of the dipole characterizing object 10 can be moreaccurately determined.

We claim:
 1. A method of determining with a device for measuringmagnetic field perturbations the bearing θ in a plane of a ferromagneticmaterial located in a region subject to an external magnetic field ofknown strength and direction within said region, where θ is the anglebetween a line from said measuring device to the location of saidferromagnetic material and a first direction, said first direction beingthe direction of said external magnetic field in said plane at thelocation of said ferromagnetic material, comprising:determining a firstcomponent in said plane of the perturbation of said external magneticfield at the site of said measuring device along said first direction;determining a second component in said plane of the perturbation of saidexternal magnetic field at the site of said measuring device along asecond direction in. said plane, wherein said second direction isorthogonal to said first direction; forming a first equation by settingsaid first component proportional to (3 cos² θ-1); forming a secondequation by setting said second component proportional to (3 sin θ cosθ); forming a ratio of said first and second equations thereby yieldinga third equation; and utilizing said third equation to determine θ.
 2. Amethod of determining with a device for measuring magnetic fieldperturbations the bearing θ in a plane of an electric currentdistribution located in a region subject to an external magnetic fieldof known strength and direction within said region where θ is the anglebetween a line from said measuring device to the location of saidelectric current distribution and a first direction, said firstdirection being the direction of said external magnetic field in saidplane at the location of said electric current distribution,comprising:determining a first component in said plane of theperturbation of said external magnetic field at the site of saidmeasuring device along said first direction; determining a secondcomponent in said plane of the perturbation of said external magneticfield at the site of said measuring device along a second direction insaid plane, wherein said second direction is orthogonal to said firstdirection; forming a first equation by setting said first componentproportional to (3 cos² θ-1); forming a second equation by setting saidsecond component proportional to (3 sin θ cos θ); forming a ratio ofsaid first and second equations thereby yielding a third equation; andutilizing said third equation to determine θ.
 3. A method of determiningwith a device for measuring electric field perturbations the bearing θin a plane of an electric charge distribution located in a regionsubject to an external electric field of known strength and directionwithin said region, where θ is the angle between a line from saidmeasuring device to the location of said charge distribution and a firstdirection, said first direction being the direction of said externalelectric field in said plane at the location of said chargedistribution, comprising:determining a first component in said plane ofthe perturbation of said external electric field at said the site ofsaid measuring device along said first direction; determining a secondcomponent in said plane of the perturbation of said external electricfield at the site of said measuring device along a second direction insaid plane, wherein said second direction is orthogonal to said firstdirection; forming a first equation by setting said first componentproportional to (3 cos² θ-1); forming a second equation by setting saidsecond component proportional to (3 sin θ cos θ); forming a ratio ofsaid first and second equations thereby yielding a third equation;utilizing said third equation to determine θ.
 4. An apparatus fordetermining the bearing θ in a plane of a ferromagnetic material locatedin a region subject to an external magnetic field of known strength anddirection within said region, where θ is, the angle between a line froma point in said plane to the location of said ferromagnetic material anda first direction, said first direction being the direction of saidexternal magnetic field in said plane at the location of saidferromagnetic material, comprising:means for determining a firstcomponent in said plane of the perturbation of said external magneticfield at said point along said first direction; means for determining asecond component in said plane of the perturbation of said externalmagnetic field at said point along a second direction in said plane,wherein said second direction is orthogonal to said first direction;means for forming a first equation by setting said first componentproportional to (3 cos² θ-1); means for forming a second equation bysetting said second component proportional to (3 sin θ cos θ); means forforming a ratio of said first and second equations thereby yielding athird equation; means for utilizing said third equation to determine θ.5. An apparatus for determining the bearing θ in a plane of an electriccurrent distribution located in a region subject to an external magneticfield of known strength and direction with in said region, where θ isthe angle between a line from a point in said plane to the location ofsaid electric current distribution and a first direction, said firstdirection being the direction of said external magnetic field in saidplane at the location of said electric current distribution,comprising:means for determining a first component in said plane of theperturbation of said external magnetic field at said point along saidfirst direction; means for determining a second component in said planeof the perturbation of said external magnetic field at said point alonga second direction in said plane, wherein said second direction isorthogonal to said first direction; means for forming a first equationby setting said first component proportional to (3 cos² θ-1); means forforming a second equation by setting said second component proportionalto (3 sin θ cos θ); means for forming a ratio of said first and secondequations thereby yielding a third equation; means for utilizing saidthird equation to determine θ.
 6. An apparatus for determining thebearing θ in a plane of an electric charge distribution located in aregion subject to an external electric field of known strength anddirection within said region, where θ is the angle between a line from apoint in said plane to the location of said charge distribution and afirst direction, said first direction being the direction of saidexternal electric field in said plane at the location of said chargedistribution, comprising:means for determining a first component in saidplane of the perturbation of said external electric field at said pointalong said first direction; means for determining a second component insaid plane of the perturbation of said external electric field at saidpoint along a second direction in said plane, wherein said seconddirection is orthogonal to said first direction; means for forming afirst equation by setting said first component proportional to (3 cos²θ-1); means for forming a second equation by setting said secondcomponent proportional to (3 sin θ cos θ); means for forming a ratio ofsaid first and second equations thereby yielding a third equation; meansfor utilizing said third equation to determine θ.
 7. A method ofdetermining with a device for measuring magnetic field perturbations thebearing θ in a plane of an object located in a region subject to anexternal magnetic field of known strength and direction within saidregion and characterized by a magnetic dipole moment, where θ is theangle between a line from said measuring device to the center of saiddipole moment and a first direction, said first direction being thedirection of said external magnetic field in said plane at said center,comprising:determining a first component in said plane of theperturbation of said external magnetic field at the site of saidmeasuring device along said first direction; determining a secondcomponent in said plane of the perturbation of said external magneticfield at the site of said measuring device along a second direction insaid plane, wherein said second direction is orthogonal to said firstdirection; forming a first equation by setting said first componentproportional to (3 cos² θ-1); forming a second equation by setting saidsecond component proportional to (3 sin θ cos θ); forming a ratio ofsaid first and second equations thereby yielding a third equation; andutilizing said third equation to determine θ.
 8. An apparatus fordetermining the bearing θ in a plane of an object located in a regionsubject to an external magnetic field of known strength and directionwithin said region and characterized by a magnetic dipole moment, whereθ is the angle between a line from a point in said plane to the centerof said dipole moment and a first direction; said first direction beingthe direction of said external magnetic field in said plane at saidcenter, comprising:means for determining a first component in said planeof the perturbation of said external magnetic field at said point alongsaid first direction; means for determining a second component in saidplane of the perturbation of said external magnetic field at said pointalong a second direction in said plane, wherein said second direction isorthogonal to said first direction; means for forming a first equationby setting said first component proportional to (3 cos² θ-1); means forforming a second equation by setting said second component proportionalto (3 sin θ cos θ); means for forming a ratio of said first and secondequations thereby yielding a third equation; means for utilizing saidthird equation to determine θ.